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arXiv · 1903.07815

Holonomy and 3-Sasakian homogeneous manifolds versus symplectic triple systems

Cristina Draper
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Abstract

Our aim is to support the choice of two remarkable connections with torsion in a 3-Sasakian manifold, proving that, in contrast to the Levi-Civita connection, the holonomy group in the homogeneous cases reduces to a proper subgroup of the special orthogonal group, of dimension considerably smaller. We realize the computations of the holonomies in a unified way, by using as a main algebraic tool a nonassociative structure, that one of symplectic triple system.

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Cristina Draper. 2019-03-19. Holonomy and 3-Sasakian homogeneous manifolds versus symplectic triple systems. https://arxiv.org/abs/1903.07815

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